Amon, while an interesting villain, given his construction of the Equalists, had a compelling enough story, but a lot of time went untold between his departure from the Southern Tribe and his introduction. There is a deeper person below the surface, but we are never exposed to deeper aspects of his character. His ability to take bending, or how he learned it, went unexplained. Zaheer, also missing such development.
On the other hand Azula being a prime example. Flashbacks through Zuko and her vision of her mother shows a mentally unstable person who wanted the approval of the mother who feared her. Even her two friends, Mai and Ty Lee, worked with Azula mainly out of fear. Such subtle writing, coupled with the insight into her character through flashbacks, made her an engaging and fun villain to watch, especially with her skills and calculating mind.